The Daily Telegraph has published a recording of a phone conversation between the Culture Secretary's adviser and one of its reporters investigating her expense claims in 2012, in which the aide "flagged up" her boss' role in the future of press regulation.
The paper has previously reported details of their conversation.
Maria Miller has denied that she had used her position overseeing the post-Leveson reforms of press regulation to ward off the Telegraph. She told the Evening Standard:
This has nothing to do with the Leveson inquiry. My concern is that any investigation is done in accordance with the rules, the Editors' Code. What I did was to contact the editor of the Telegraph directly to express my concern at the way his investigation was being undertaken.
The journalist hadn't contacted my office first. She had doorstepped a member of my family, a person who is not in public life, a person ill-equipped to deal with national media inquiries on my behalf.
Mrs Miller's special adviser, Joanna Hindley, reportedly told Telegraph reporters investigating her expenses: "Maria has obviously been having quite a lot of editors' meetings around Leveson at the moment. I am just going to flag up that connection for you to think about."
Maria Miller has said one of the two audits into her expenses had been carried out by former civil servant Sir Thomas Legg - who was called in to review all MPs' claims at the height of the expenses scandal - and the other by the Conservative Party.
Mrs Miller claimed second home allowances of £90,718 - almost the maximum permitted - between 2005 and 2009 towards mortgage payments, bills and other costs relating to a house where her parents had apparently been living since 1996.
Asked by the Evening Standard whether Sir Thomas was aware that her parents were living at her designated second home, Mrs Miller said: "I obviously spoke to the Fees Office about my claims and they were happy that everything was in order."